Math 135Q-01
Fall 2006
 
C. Vinsonhaler
MSB 316
860-486-3944
vinsonhaler@math.uconn.edu

 

Course Parameters
Goals and Expectations
Homework
Outline
Academic Integrity
Sample Exams
Related Links  

 

Course Parameters

Text: Calculus, Single Variable, by Hughes-Hallett, Gleason, et al, 4th Edition


Class Meetings :  F 12-12:50, MSB 407       TTh 12:30 - 1:45, MSB 303

Office Hours :  F 1-2, T Th 2-3 and by appointment

Credit limitations: not open for students who have passed Math 112, 115, or 120.

Grading:  Homework & Quizzes - 20%, Two exams - 20% each, Final - 40%

Notes on the calendar: Fall semester classes begin Monday, August 28, and end Friday, December 8.  
September 11 is the last day to drop without a W. October 30 is the last day to drop.

First Hour Exam:  October 3.
Second Hour Exam:  November 14

Goals.     Our goal is to learn the basic concepts and techniques of differential calculus, and also to gain an appreciation for the beauty and utility of this marvelous subject.

Expectations.
    1.  I expect you to come to class, on time. You are responsible for everything that happens in class whether or not you attend. If you must miss a class, you must notify me in advance in order to be allowed to make up the work (phone, email, note in mailbox, or verbal communication).
    2.  I expect you to work outside of class, somewhere on the order of 6-8 hours per week. Homework is work to be done at home - we will not spend much class time going over homework exercises. You are welcome and encouraged to work together on homework and to get help from other sources (friends, instructor, Calculus Center, Q-Center), but you must write up solutions yourself.
    3. I expect your homework submissions to be neat and to include explanations with full sentences, correct spelling and grammar. Show your work. Mathematics is not just scribbling with the answer circled at the end. You need to communicate the brilliance of your insights to others.
    4.  No late assignments will be accepted. No make-up exams will be given. The only exceptions to this rule may be made if you notify your teacher in advance with a valid excuse.

There are three categories of home work in Math 135:

  1. Exercises: These should be worked out but not handed in. Students can go online to check their work with e-Grade.
  2. Problems: These are to be written up carefully and handed in for grading.
  3. Team problems: These are to be worked on and discussed in a team setting, the solutions written up and then handed in for grading as directed by the instructor.

 

Exercises (in text & e-Grade)
(not collected)

Problems
(graded)

Team Problems
(graded)

 

Chapter 1

 

 

 

 

Section 1.1

4,7,10,12,16,18,21

28,32,33,36

37

 

Section 1.2

3,4,5

14,16,17,18,22,28

31

 

Section 1.3

1ab,7,16,21,27,29

39,40,41,43,47,53

 

 

Section 1.4

3,6,10,11,26,29,30

32,37,40

46, 34 on page 59

 

Section 1.5

13,17,19,25,28,29,32

39,41,43

40,42

 

Section 1.6

7,8,10,11acd

15,18,22,24

19, 27

 

Section 1.7

3,9,10

17,19,23

 

 

Section 1.8

1bc,2,3,14,16,21

31,35,43,44

45,48

 

Chapter 2

 

 

 

 

Section 2.1

3,6,7,9

11,12,13,16

14 (explain)

 

Section 2.2

1,9,10  

12,13,14,16,29,35,40

2 on page 108

 

Section 2.3

1,8,11a,16

29,30,31,33,35,36,40

37 (explain)

 

Section 2.4

1,3,6,9

11,13,15,21

16,30 on page 105

 

Section 2.5

1,5,6,7,9,11,13

16,20

23

 

Section 2.6

1,3 

7,15

13

 

Chapter 3

 

 

 

 

Section 3.1

all odd (e-Grade: 3,7,17,21,23,25,27,31,33,35)

52,55,56,58,63

62

 

Section 3.2

all odd (e-Grade: 3,5,7,9,11,15,23)

38,39,40,42

43

 

Section 3.3

all odd (e-Grade: 3,7,9,15,21,23,27,29)

31,36,44,46,50

53

 

Section 3.4

all odd (e-Grade: 3,9,11,15,17,27,35,41)

53,63,66,71,78

79

 

Section 3.5

all odd (e-Grade: 9,21,25,27,31,35)

40,44,49

48

 

Section 3.6

all odd (e-Grade:1,11,15,23,25,29)

39,44,58

43, 97 (pg 162)

 

Section 3.7

all odd (e-Grade:3,5,11,13,21,23,25)

29,31

28

 

Section 3.9

1,6

10,21,25

18

 

Section 3.10

2,4,5,8

11,14,16

22

 

Chapter 4

 

 

 

 

Section 4.1

3a,7,18,19,20

24,27,2835,41,43,45

38 (explain)

 

Section 4.2

9,10,14,15

21,23,29

28

 

Section 4.3

5b,11,15,18 

19,20,23,27,31,35

30

 

Section 4.5

4,8

11,16,18,20,23,26,28,32,34

25,27

 

Section 4.6

1,5,10

15,20,21,24,27,29

34

 

Chapter 5

 

 

 

 

Section 5.1

3,7,11

15,16,26

 

 

Section 5.2

1ab,4,7,14

22,27,28

 

 

Section 5.3

3,6,11

19,21,24,25,28,31

18,34

 

Section 5.4

3,7,8,11

15,17,22,28,31,35, 44 (pg 277)

43 (pg 277)

 

Chapter 6

 

 

 

 

Section 6.1

4,5,7

13,15,19,23,25

18

 

Section 6.2

17,25,38,48,57,65,70

73,77,80

 

 

 

OUTLINE   

This is a guide only. Topics may vary according to our progress in class.
 Math 135 Outline - Fall 2006

Date

Section

Topic

8/29

1.1

Functions and Change

8/31

1.2

Exponential Functions

9/1

1.3

New Functions From Old

9/5

No Class

Labor Day

9/7

1.4

Logarithmic Functions

9/8

1.5, 1.6

Trigonometric Functions, Powers, Polynomials, and Rational Functions

9/12

1.7

Introduction to Continuity

9/14

1.8

Limits

9/15

2.1

How Do We Measure Speed

9/19

2.2

The Derivative At A Point

9/21

2.3

The Derivative Function

9/22

2.4

Interpretations of the Derivative

9/26

2.5

The Second Derivative

9/28

2.6

Differentiability

9/29

3.1

Powers and Polynomials

10/3

3.2

The Exponential Function

10/5

3.3

The Product and Quotient Rules

10/6

Review for Exam I

 

10/10

Review for Exam I

Exam I is Oct. 11, 6-8 PM

10/12

3.4

The Chain Rule

10/13

3.5

The Trigonometric Functions

10/17

3.6

The Chain Rule and Inverse Functions

10/19

3.7

Implicit Functions

10/20

3.9, 3.10

Linear Approximations and the Derivative, Theorems about Differentiable Functions

10/24

In Class Gateway Exam

 

10/26

3.10

Theorems About Differentiable Functions

10/27

4.1

Using First and Second Derivative

10/31

4.2

Families of Curves

11/2

4.3

Optimization

11/3

4.5

Optimization and Modeling

11/7

4.6

Rates and Related Rates

11/9

4.7

L'Hopital's Rule, Growth, and Dominance

11/10

Review for Exam 2

End of Open Gateway Exam Period.

11/14

Review for Exam 2

Exam 2 is on Nov. 15, 6-8 PM

11/16

4.8

Parametric Equations

11/17

5.1

How Do We Measure Distance Traveled?

11/21

No Class

Thanksgiving

11/23

No Class

Thanksgiving

11/24

No Class

Thanksgiving

11/28

5.2

The Definite Integral

11/30

5.3

The Fundamental Theorem and Interpretations

12/1

5.4

Theorems About Definite Integrals

12/5

6.1, 6.2

Antiderivataive Graphically and Numerically

12/7

6.2, 6.4

Constructing Antiderivative Analytically, Second Fundamental Theorem

12/8

 

Review for final exam

 


                                              A note on the exercises

The above outline contains a  list of proposed exercises for each section of the text we discuss. Many of them are odd-numbered, so the answer appears in the back of the book. I suggest that you not look at the answer until you have given the problem your "best shot." For additional challenges, tackle the Problems Plus section at the end of each chapter.

 

                                          

Math Center Help & Tutoring

The Math Center is open Sun-Thurs  12  noon- 10 P.M. to help students with all mathematics courses through MATH 116. 

The Q-Center in CUE 123 is open 4-8PM, Sunday-Wednesday, for tutoring on Math 115.                      


                                                               Academic Integrity

("Beginning with the fall semester 2000, syllabi should include a warning about academic misconduct,
particularly cheating and plagiarism."   See http://vm.uconn.edu/~dosa8/code2.html )

"A fundamental tenet of all educational institutions is academic honesty; academic work depends upon respect for and acknowledgement of the research and ideas of others. Misrepresenting someone else's work as one's own is a
serious offense in any academic setting and it will not be condoned."

"Academic misconduct includes, but is not limited to, providing or receiving assistance in a manner not authorized by the instructor in the creation of  work to be submitted for academic evaluation (e.g. papers, projects, and
examinations); any attempt to influence improperly (e.g. bribery, threats) any member of the faculty, staff, or administration of the University in any matter pertaining to academics or research; presenting, as one's own, the ideas or words of another for academic evaluation; doing unauthorized academic work for which another person will receive credit or be evaluated;
and presenting the same or substantially the same papers or projects in two or more courses without the explicit permission of the instructors involved."

"A student who knowingly assists another student in committing an act of academic misconduct shall be equally accountable for the violation, and shall be subject to the sanctions and other remedies described in The Student Code."
 
 


EXAM 1  REVIEW

Functions:  Functions from other functions, fog, f(x-2)+1, etc.

Limits:  calculations, formal definition, proof in linear case, epsilon-delta graphs, Squeeze Theorem

Continuous: definition, graphical interpretation, Intermediate Value Theorem
Derivatives:  slope of tangent line, velocity, rate of change, limit definition, calculate from algebra and from graphs, derivative implies continuous  

Example of  epsilon-delta proof. Prove that the limit as x approaches 4 of 2x-7 is 1.  Use e for epsilon and d for delta.

Given e > 0, we want to make abs(2x-7 - 1) < e. Equivalently, abs(2x-8) < e or  2abs(x-4) < e or abs(x-4) < e/2.
Take d = e/2. Then 0 < abs(x-4) < d guarantees abs(2x-7 - 1) < e .

 

Sample Exam 1, Fall 2005, Answers

1.     FFFTFFT

2.     y = 2(x-1)/(e2 – 1)

3.     (a)  P = 100,004(1.08)t/2 ; y = 105000 + 5325t

(b) will be adequate

(c  ) until around 2001

      4.  Done in class

      5.  V = pr2(36-2r)/6

      6.  y = -8sin(pt/6) – 18, or y = 8sin((p/6)(t-6)) - 18

      7.  (a)  (1/3)x/5     (b)  7(x+2)(x-3)(x-5)/30

      8.  (a)  y = -5x + 11;   y = -4x + 9

            (b)  3.5 ;  3

            (c )  Skip this part

      9. (a) t = 4    (b)  1000    (c)  in class

     10.  (a)  AJ  (b) G   (c) BDEJ  (d)  None   (e)  CI

     11.  Graph is not labeled correctly

 

 

Exam 1, Fall, 2002 (hard copy available)

1.  Done in class
2(a).  7   (b)  - infinity
3.  Done in class
4.  Done in class, delta = .76
5.  Done in class   Must be continuous at x = 3.  Need not have a derivative at x =2.
6.  9 mph
7.  the derivative is the line y = -.5x - 1


Exam 1, Spring 2001

1(a). -4,0,3   (b)  4   (c)  DNE   (d)  0   (e)  no, g(1) = 0
2(a).  x less or equal to 9   (b)  4 < x <= 9    (c)  x  greater or equal 4, not equal 5
3.  This one should be easy
4(a)  DNE   (b)  + infinity   (c)  + infinity   (d)  1/2
5.  Use -x^2  < x^2cos(1/x) < x^2
6(a)  - infinity  (b)  - infinity   (c)  0
7.  Standard epsilon-delta proof.  In this case delta = 5/3 epsilon
8(a)  jump discontinuity, one-sided limits differ    (b)  g(1) is not defined   (c)  g(4) is not equal to lim g(x) as x approaches 4
9.  If  f(x) = x^3 - 3,  then f(0) = -3  and  f(2) = 5. By ICT

Exam 2 Review Topics

Practice Exam 2
Answers to Practice Exam 2

Help with homework :   Hotmath

Final Review Topics:

  • Concepts: functions, limits (epsilon and delta), continuity (Intermediate Value Theorem), derivatives (Mean Value Theorem), integrals (Fundamental Theorem of Calculus)
  •  Skills: formal proof of limits for linear functions, calculate limits and derivatives using the limit definition, product, quotient  and chain rule, position-velocity-acceleration, rates of change, implicit differentiation, tangent lines, related rates, Max-Min on an interval, linear approximation, Newton's method, properties of graphs, optimization, Riemann sums and numerical integration, substitution,area, volume of revolution.

Sample final

(My) Answers to Sample final (numerical only).

1. 1/4,   2.   3.   4.  3/pi   5.  1.9975  6.  4   7.  8pi/5   8(a)  1/2  (b)  1   (c)  8

9.  7/3   10.  9   11(a)  increasing x > 1; decreasing x < 1.  

11(b)  concave up x < 0 or x > 2/3;  concave down 0 < x < 2/3  11(c)  x = 1 relative min

11(d)  x = 0, 2/3  inflection points    12.  length = 25, width = 10

Fall 2003 FINAL


Fall 2003 FINAL Answers

Related Links
    Riemann Sums